Geometrical Proof Flashcards

All 5 cards in this deck

In a geometrical proof, what must you write alongside each statement?

A reason, e.g. "angles on a straight line add to $180^\circ$" or "base angles of an isosceles triangle are equal".

What are the steps to set out a chain of reasoning in a geometrical proof?

e.g. isosceles triangle $ABC$ with $AB=AC$ and $D$ the midpoint of $BC$: show angle $B=$ angle $C$

1. State the facts with reasons: $AB=AC$ (isosceles), $BD=DC$ ($D$ is the midpoint), $AD$ is common
2. Name the criterion: SSS, so triangles $ABD$ and $ACD$ are congruent
3. Conclude: corresponding angles are equal, so angle $B=$ angle $C$.

True or false? Checking that a geometrical result works for one particular triangle proves it.

False. A proof must use general facts and reasons that hold for every case.

Which known result links the three sides of a right-angled triangle and can be quoted in a proof?

Pythagoras' theorem: $a^2+b^2=c^2$, where $c$ is the hypotenuse.

Which properties of a parallelogram can you quote as reasons in a proof?

Opposite sides are equal and parallel, and opposite angles are equal.